diff --git a/graph/breadth_first_tree.h b/graph/breadth_first_tree.h
new file mode 100644
index 0000000..296ef04
--- /dev/null
+++ b/graph/breadth_first_tree.h
@@ -0,0 +1,28 @@
+#ifndef BREADTH_FIRST_TREE_H_
+#define BREADTH_FIRST_TREE_H_
+
+#include "digraph.h"
+
+namespace graph {
+
+template<typename T>
+class BreadthFirstTree : public Digraph<T> {
+public:
+  BreadthFirstTree() = default;
+
+  BreadthFirstTree(std::map<T, std::set<T>> G, T root)
+    : BreadthFirstTree<T>(Digraph<T>(G), root) {}
+
+  BreadthFirstTree(Digraph<T> G, T root);
+
+  T root;
+};
+
+template<typename T>
+BreadthFirstTree<T>::BreadthFirstTree(Digraph<T> G, T root) {
+  this->adjMatrix = algo::BreadthFirstSearch<T>(G.adjMatrix).execute(root);
+}
+
+} // namespace graph
+
+#endif
\ No newline at end of file
diff --git a/graph/digraph.h b/graph/digraph.h
index c10f1b6..4880d6f 100644
--- a/graph/digraph.h
+++ b/graph/digraph.h
@@ -2,9 +2,7 @@
 #define DIGRAPH_H_
 
 #include "graph.h"
-
-#include <algorithm>
-#include <ranges>
+#include "algorithm/breadth_first_search.h"
 
 namespace graph {
 
@@ -13,24 +11,49 @@ class Digraph : public Graph<T> {
 public:
   Digraph() = default;
 
-  Digraph(std::map<T, std::set<T>> digraph);
+  Digraph(std::map<T, std::set<T>> G);
+
+  // Return true if there is a path from u to v
+  bool contains(const T& u, const T& v);
+
+  // Add edge e(u,v)
+  void insert(const T& u, const T& v);
+
+  // Remove edge e(u,v)
+  void remove(const T& u, const T& v);
 
   // Reverse graph directions
   auto reverse();
 };
 
 template<typename T>
-Digraph<T>::Digraph(std::map<T, std::set<T>> digraph) {
-  Graph<T>::adjMatrix = digraph;
+Digraph<T>::Digraph(std::map<T, std::set<T>> G) {
+  this->adjMatrix = G;
+}
+
+template<typename T>
+bool Digraph<T>::contains(const T& u, const T& v) {
+  return algo::BreadthFirstSearch<T>().query(u, v);
+}
+
+template<typename T>
+void Digraph<T>::insert(const T& u, const T& v) {
+  this->adjMatrix[u].insert(v);
+  this->adjMatrix[v];
+}
+
+template<typename T>
+void Digraph<T>::remove(const T& u, const T& v) {
+  this->adjMatrix[u].erase(v);
 }
 
 template<typename T>
 auto Digraph<T>::reverse() {
   std::map<T, std::set<T>> revMatrix;
   
-  for (const auto& v : Graph<T>::adjMatrix) {
-    for (const auto& u : v.second) {
-      revMatrix[u].insert(v.first);
+  for (const auto& u : this->adjMatrix) {
+    for (const auto& v : u.second) {
+      revMatrix[v].insert(u.first);
     }
   }
 
diff --git a/graph/graph.h b/graph/graph.h
index f688e96..e67bd27 100644
--- a/graph/graph.h
+++ b/graph/graph.h
@@ -3,38 +3,38 @@
 
 #include <map>
 #include <set>
-#include <iostream>
+#include <ostream>
 
 namespace graph {
 
+// Forward declerations
+template<typename T> class Graph;
+template<typename T> std::ostream& operator<<(std::ostream& os, Graph<T>& G);
+
 template<typename T>
 class Graph {
 public:
   ~Graph();
+  
+  // Return true if there is a path from u to v
+  virtual bool contains(const T& u, const T& v) = 0;
 
   // Add edge e(u,v)
-  virtual void insert(const T& u, const T& v);
-
-  // Return true if e(u,v) exists
-  virtual bool contains(const T& u, const T& v);
-
-  // Return true if vertex u exists
-  virtual bool contains(const T& u);
+  virtual void insert(const T& u, const T& v) = 0;
 
   // Remove edge e(u,v)
-  virtual void remove(const T& u, const T& v);
+  virtual void remove(const T& u, const T& v) = 0;
 
   // Return num. of vertices
-  virtual std::uint16_t V();
+  std::uint16_t V();
 
   // Return num. of edges
-  virtual std::uint16_t E();
-
-  // Output graph
-  virtual void output();
+  std::uint16_t E();
 
   // Adjacency matrix representation
   std::map<T, std::set<T>> adjMatrix;
+
+  friend std::ostream& operator<<<>(std::ostream& os, Graph<T>& G);
 };
 
 template<typename T>
@@ -42,27 +42,6 @@ Graph<T>::~Graph() {
   adjMatrix.clear();
 }
 
-template<typename T>
-inline void Graph<T>::insert(const T& u, const T& v) {
-  Graph<T>::adjMatrix[u].insert(v);
-  Graph<T>::adjMatrix[v];
-}
-
-template<typename T>
-bool Graph<T>::contains(const T& u, const T& v) {
-  return adjMatrix[u].contains(v);
-}
-
-template<typename T>
-bool Graph<T>::contains(const T& u) {
-  return adjMatrix.contains(u);
-}
-
-template<typename T>
-void Graph<T>::remove(const T& u, const T& v) {
-  adjMatrix[u].erase(v);
-}
-
 template<typename T>
 std::uint16_t Graph<T>::V() {
   return static_cast<std::uint16_t>(adjMatrix.size());
@@ -78,14 +57,18 @@ std::uint16_t Graph<T>::E() {
 }
 
 template<typename T>
-void Graph<T>::output() {
-  for (const auto& v : adjMatrix) {
-    for (const auto& u : v.second) {
-      std::cout << v.first << "->" << u << '|';
+std::ostream& operator<<(std::ostream& os, Graph<T>& G) {
+  os << "V: " << G.V() << " E: " << G.E() << '\n';
+  for (const auto& u : G.adjMatrix) {
+    if (!u.second.empty()) {
+      for (const auto& v : u.second) {
+        os << u.first << "->" << v << ' ';
+      }
+      os << '\n';
     }
-    std::cout << '\n';
   }
-  std::cout << '\n';
+  os << '\n';
+  return os;
 }
 
 } // namespace graph
diff --git a/graph/scc.h b/graph/scc.h
index 83760e9..94592e2 100644
--- a/graph/scc.h
+++ b/graph/scc.h
@@ -3,8 +3,6 @@
 
 #include "digraph.h"
 
-#include <ranges>
-
 namespace graph {
 
 template<typename T>
@@ -12,22 +10,34 @@ class SCC : public Digraph<T> {
 public:
   SCC() = default;
 
-  SCC(std::map<T, std::set<T>> scc)
-    : Digraph<T>::Digraph(scc) { proxy = scc.begin()->first; }
+  SCC(std::map<T, std::set<T>> G, T id) : Digraph<T>(G), id(id) { normalize(); }
 
-  //
-  T representative() { return proxy; };
+  SCC(Digraph<T> G, T id) : id(id) { normalize(); }
+
+  T id;
 
   bool operator==(const SCC& o) const;
 private:
-  // Each SCC has a representative vertex that helps
-  // answer strong connectivity queries in O(1) time
-  T proxy;
+  // For every vertex in the SCC, if there is an edge between an in-scc vertex
+  // and an out-scc vertex erase the edge between them and the out-scc vertex
+  void normalize();
 };
 
+template<typename T>
+void SCC<T>::normalize() {
+  for (const auto& u : this->adjMatrix) {
+    for (const auto& v : u.second) {
+      if (!this->adjMatrix.count(v)) {
+        this->adjMatrix[u.first].erase(v);
+        this->adjMatrix.erase(v);
+      }
+    }
+  }
+}
+
 template<typename T>
 bool SCC<T>::operator==(const SCC& o) const{
-  return proxy == o.proxy;
+  return id == o.id;
 }
 
 }; // namespace graph
diff --git a/test/graph_test.cc b/test/graph_test.cc
index e6d957d..5c8be0d 100644
--- a/test/graph_test.cc
+++ b/test/graph_test.cc
@@ -10,48 +10,63 @@ using namespace graph;
 TEST_SUITE("Graph") {
 
   TEST_CASE("Digraph::reverse") {
-    // 1 --> 2 --> 4 --> 1
-    //       2 --> 3 --> 5 --> 7 --> 3
-    //                   5 --> 9 --> 6 --> 8 --> 9
+    // 1 --> 2 --> 3 --> 1
+    //             3 --> 4 --> 5 --> 3
+    //       2 --> 6 --> 7 --> 8 --> 6
+    //                   7 --> 9
+    //             6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9
+    //                                       12 --> 10
     Digraph<std::uint16_t> G;
     G.insert(1, 2);
     G.insert(2, 3);
-    G.insert(2, 4);
-    G.insert(3, 5);
-    G.insert(4, 1);
-    G.insert(5, 7);
-    G.insert(5, 9);
-    G.insert(6, 8);
-    G.insert(7, 3);
-    G.insert(8, 9);
-    G.insert(9, 6);
+    G.insert(3, 1);
+    G.insert(3, 4);
+    G.insert(4, 5);
+    G.insert(5, 3);
+    G.insert(2, 6);
+    G.insert(6, 7);
+    G.insert(7, 8);
+    G.insert(7, 9);
+    G.insert(8, 6);
+    G.insert(6, 9);
+    G.insert(9, 10);
+    G.insert(10, 11);
+    G.insert(11, 12);
+    G.insert(12, 13);
+    G.insert(13, 9);
+    G.insert(12, 10);
 
-    REQUIRE_EQ(G.adjMatrix.size(), 9);
+    REQUIRE_EQ(G.adjMatrix.size(), 13);
 
-    auto R = G.reverse();
+    auto reverse = G.reverse();
 
-    std::map<std::uint16_t, std::set<std::uint16_t>> X = {
-      {1, {4}},
+    std::map<std::uint16_t, std::set<std::uint16_t>> expected = {
+      {1, {3}},
       {2, {1}},
-      {3, {2, 7}},
-      {4, {2}},
-      {5, {3}},
-      {6, {9}},
-      {7, {5}},
-      {8, {6}},
-      {9, {5, 8}}
+      {3, {2, 5}},
+      {4, {3}},
+      {5, {4}},
+      {6, {2, 8}},
+      {7, {6}},
+      {8, {7}},
+      {9, {6, 7, 13}},
+      {10, {9, 12}},
+      {11, {10}},
+      {12, {11}},
+      {13, {12}}
     };
     
-    CHECK_EQ(R, X);
+    CHECK_EQ(reverse, expected);
   }
 
   TEST_CASE("Graph::V and Graph::E") {
     // 1 --> 2 --> 3 --> 1
     //             3 --> 4 --> 5 --> 3
     //       2 --> 6 --> 7 --> 8 --> 6
+    //                   7 --> 9
     //             6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9
     //                                       12 --> 10
-    Graph<std::uint16_t> G;
+    Digraph<std::uint16_t> G;
     G.insert(1, 2);
     G.insert(2, 3);
     G.insert(3, 1);
diff --git a/test/tree_test.cc b/test/tree_test.cc
deleted file mode 100644
index fb27811..0000000
--- a/test/tree_test.cc
+++ /dev/null
@@ -1,36 +0,0 @@
-#include <doctest/doctest.h>
-
-#include "tree/breadth_first_tree.h"
-
-using namespace graph;
-using namespace tree;
-
-TEST_SUITE("Tree") {
-  TEST_CASE("Breadth First Tree") {
-
-    // 1 --> 2 --> 5 --> 7 --> 2
-    // 1 --> 4 --> 3 --> 1
-    //       4 --> 6 --> 3
-    Digraph<std::uint16_t> G;
-    G.insert(1, 2);
-    G.insert(1, 4);
-    G.insert(2, 5);
-    G.insert(3, 1);
-    G.insert(4, 3);
-    G.insert(4, 6);
-    G.insert(5, 7);
-    G.insert(6, 3);
-    G.insert(7, 2);
-
-    BreadthFirstTree<std::uint16_t> tree(G, 1);
-
-    std::map<std::uint16_t, std::set<std::uint16_t>> exp = {
-      {1, {2, 4}},
-      {2, {5}},
-      {4, {3, 6}},
-      {5, {7}}
-    };
-
-    CHECK_EQ(tree.adjMatrix, exp);
-  }
-}
\ No newline at end of file
diff --git a/tree/breadth_first_tree.h b/tree/breadth_first_tree.h
deleted file mode 100644
index 0a3beeb..0000000
--- a/tree/breadth_first_tree.h
+++ /dev/null
@@ -1,29 +0,0 @@
-#ifndef BREADTH_FIRST_TREE_H_
-#define BREADTH_FIRST_TREE_H_
-
-#include "directed_rooted_tree.h"
-#include "algorithm/breadth_first_search.h"
-using namespace graph;
-
-namespace tree {
-
-template<typename T>
-class BreadthFirstTree : public DirectedRootedTree<T> {
-public:
-  BreadthFirstTree() = default;
-
-  BreadthFirstTree(Digraph<T> G, T root);
-
-  BreadthFirstTree(std::map<T, std::set<T>> G)
-    : DirectedRootedTree<T>::DirectedRootedTree(G) {}
-};
-
-template<typename T>
-BreadthFirstTree<T>::BreadthFirstTree(Digraph<T> G, T root) {
-  auto bfs = algo::BreadthFirstSearch<T>(G).execute(root);
-  this->adjMatrix = bfs;
-}
-
-} // namespace tree
-
-#endif
\ No newline at end of file
diff --git a/tree/directed_rooted_tree.h b/tree/directed_rooted_tree.h
deleted file mode 100644
index c8b77ce..0000000
--- a/tree/directed_rooted_tree.h
+++ /dev/null
@@ -1,20 +0,0 @@
-#ifndef DIRECTED_ROOTED_TREE_H_
-#define DIRECTED_ROOTED_TREE_H_
-
-#include "tree.h"
-using namespace graph;
-
-namespace tree {
-
-template<typename T>
-class DirectedRootedTree : public Tree<T> {
-public:
-  DirectedRootedTree() = default;
-
-  DirectedRootedTree(std::map<T, std::set<T>> G)
-    : Tree<T>::Tree(G) {}
-};
-
-} // namespace tree
-
-#endif
\ No newline at end of file
diff --git a/tree/tree.h b/tree/tree.h
deleted file mode 100644
index 44447ce..0000000
--- a/tree/tree.h
+++ /dev/null
@@ -1,19 +0,0 @@
-#ifndef TREE_H_
-#define TREE_H_
-
-#include "graph/digraph.h"
-using namespace graph;
-
-namespace tree {
-
-template<typename T>
-class Tree : public Digraph<T> {
-public:
-  Tree() = default;
-
-  Tree(std::map<T, std::set<T>> G) : Digraph<T>::Digraph(G) {}
-};
-
-} // namespace tree
-
-#endif
\ No newline at end of file